A smart manager would not hold a position that is 50% of daily volume. I use daily volume restrictions when trading. I never hold more that 5% of daily volume and that is high in my opinion.

The only option I could see at this point is to hedge a large chunk of your position and start selling small chunks of your position each day, lets say 5% of market volume a day. If the instrument does not have options to hedge, you may try to find strong correlated instrument and hedge with its options. You will not be able to hedge "perfectly" but it will remove a large amount of risk.